👉 Try now NerdPal! Our new math app on iOS and Android

# Express in terms of sine and cosine Calculator

## Get detailed solutions to your math problems with our Express in terms of sine and cosine step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Difficult Problems

1

Solved example of express in terms of sine and cosine

$\frac{1-\tan\left(x\right)}{1+\tan\left(x\right)}$
2

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{1+\frac{-\sin\left(x\right)}{\cos\left(x\right)}}{1+\tan\left(x\right)}$
3

Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator

$\frac{\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}}{1+\tan\left(x\right)}$
4

Divide fractions $\frac{\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}}{1+\tan\left(x\right)}$ with Keep, Change, Flip: $\frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}$

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)\left(1+\tan\left(x\right)\right)}$
5

Multiply the single term $\cos\left(x\right)$ by each term of the polynomial $\left(1+\tan\left(x\right)\right)$

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)+\tan\left(x\right)\cos\left(x\right)}$

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{\sin\left(x\right)}{\cos\left(x\right)}\cos\left(x\right)$

Multiplying the fraction by $\cos\left(x\right)$

$\sin\left(x\right)$
6

Applying the trigonometric identity: $\tan\left(\theta\right)\cdot\cos\left(\theta\right)=\sin\left(\theta\right)$

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)+\sin\left(x\right)}$

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)+\sin\left(x\right)}$